Method of measuring motor constant for induction motor

ABSTRACT

A method of measuring a motor constant is provided in a vector control apparatus for an induction motor. A voltage output phase θv is set at a previously set arbitrary phase. Prior to applying a current, a current command is fed to operate the vector control apparatus with a proportional-plus-integral controller being set operative. After conduction for a predetermined time, the gain of the proportional-plus-integral controller is set to zero to maintain an integrated value constant and accordingly fix a voltage command value. In this state, a current command value and a detected current value are measured. This measurement is performed at two levels of current, and a primary resistance value (or a line-to-line resistance value) is derived from the slope.

This application is the U.S. National Phase under 35 U.S.C. §371 ofInternational Application PCT/JP01/05844, filed Jul. 5, 2001, whichclaims priority to Japanese Patent Application No. 2000-212896, filedJul. 13, 2000. The International Application was published under PCTArticle 21(2) in a language other than English.

TECHNICAL FIELD

The present invention relates to a method of measuring a motor constantfor an induction motor.

BACKGROUND ART

There is software for controlling an inverter, which includes a methodof determining a motor constant by conducting a winding resistancemeasurement, a lock test and a no-load test, as shown in JEC-37 (PriorArt Example 1). Also, JP-A-7-55899 discloses a method of tuning aconstant of an induction motor while the induction motor remainsinoperative (Prior Art Example 2). In this method, a single-phase ACcurrent is supplied to an induction motor, and a detected d-axis currentvalue or a detected q-axis current value is expanded in Fourier seriesto determine a constant of the induction motor. Here, d-q axiscoordinates are rotating coordinates which rotate at the same velocityas a rotating magnetic field of the motor.

The method shown in Prior Art Example 1 is not suitable for automaticmeasurements by means of driving an inverter because it involvesoperations for fixing a rotor of an induction motor and releasing thefixation between a lock test and a no-load current test.

Also, in the no-load current test, the induction motor must be operatedalone, so that if a load has been coupled thereto, an operation isrequired for once disconnecting the load to leave the motor alone, thusincurring a problem of a low efficiency.

Prior Art Example 2 needs complicated software because a single-phase ACcurrent is applied and Fourier series expansion is utilized for thedetermination of a motor constant, thus requiring a long softwareprocessing time, and a large memory capacity for the software.

DISCLOSURE OF THE INVENTION

It is therefore an object of the present invention to provide a methodof measuring a motor constant for an induction motor which comprisesaccurately tuning the constant of the induction motor even when a loadis coupled to the induction motor, and involves only simple processingtherefor.

The present invention is directed to a motor vector control apparatusfor a motor which separates a motor primary current into a fluxcomponent (d-axis component) and a torque component (q-axis component),and has a d-axis current proportional-plus-integral controller whichreceives a current command for a d-axis component and a detected currentvalue of the d-axis component for controlling a deviation between bothto reduce to zero; a first adder for adding an output of thisproportional-plus-integration controller and an arbitrary d-axisauxiliary voltage command value to derive a d-axis voltage commandvalue; a q-axis current proportional-plus-integral controller whichreceives a current command for a q-axis component and a detected currentvalue of the q-axis component for controlling a deviation between bothto reduce to zero; a second adder for adding an output of thisproportional-plus-integral controller and an arbitrary q-axis auxiliaryvoltage command value to derive a q-axis voltage command value; and apower converter for calculating a magnitude v_ref and a voltage phase θvof a voltage command from the d-axis voltage command value and theq-axis voltage command value, and converting a DC current to athree-phase AC current based on the magnitude of the voltage command andthe phase of the voltage command to provide the three-phase AC current.The vector control apparatus is configured to convert the motor to anequivalent circuit of a three-phase Y (star) connection to handle andcontrol the motor.

The vector control apparatus is operated by applying the same with ad-axis current command value id_ref1 and a q-axis current command valueiq_ref1 previously set at arbitrary fixed values as first commandvalues, and with the d-axis auxiliary voltage command vd_ref_c and theq-axis auxiliary voltage command value vq_ref_c both set at zero. Afterthe lapse of a previously set first time, a proportional gain of thed-axis proportional-plus-integral controller and a proportional gain ofthe q-axis proportional-plus-integral controller are set to zero. Afterthe lapse of a previously set second time from this time, the voltagecommand:v_ref=√{square root over ((vd_ref² +vq_ref²))}is created from the d-axis voltage command vd_ref and the q-axis voltagecommand vq_ref, and the detected current value:i _(—) fd=√{square root over ((id _(—) fd ² +iq _(—) fb ²))}is created from the d-axis detected current value id_fb and the q-axisdetected current value iq_fb. An average of v_ref and an average of i_fbrecorded within an arbitrary time during the second time are set asfirst data v_ref1, i_fb1, respectively.

Next, the vector control apparatus is operated, after the gains of bothproportional-plus-integral controllers are returned to original values,by applying a d-axis current command value id_ref2 and a q-axis currentcommand value iq_ref2 previously set at arbitrary fixed values as secondcommand values, and applying the d-axis auxiliary voltage command valuevd_ref_c and the q-axis auxiliary voltage command value vq_ref_c set atzero. After the lapse of the previously set first time, the proportionalgain of the d-axis current proportional-plus-integral controller and theproportional gain of the q-axis current proportional-plus-integralcontroller are set to zero. After the lapse of a previously set secondtime from this time, a primary resistance of the motor is calculated inaccordance with:R1={v_ref2−v_ref1)/√{square root over (3})}/(i _(—) fb2−i _(—) fb1)using an average of v_ref and an average of i_fb recorded within anarbitrary time during the second time as second data v_ref2, i_fb2,respectively, and a line-to-line resistance of the motor is calculatedin accordance with R_(L-L)=2·R1.

Alternatively, the gains and outputs of the proportional-plus-integralcontrollers, the d-axis auxiliary voltage command and the q-axisauxiliary voltage command are set to zero, a previously set arbitraryfixed value is set to a voltage phase θv, and a magnitude vref of thevoltage command is given by v_ref=vamp·sin(2·π·fh·t), where fh is aproper frequency 1/10 or more as high as a rated operation frequency ofthe motor, and vamp is a voltage amplitude. Vamp is incrementally ordecrementally adjusted while monitoring the current value i_fb suchthat:i _(—) fb=√{square root over ((id _(—) fb ² +iq _(—) fb ²))}calculated from a d-axis detected current value id_fb and a q-axisdetected current value iq_fb reaches a first set current value. Afteri_fb reaches the first set current value, an average of an absolutevalue of the magnitude v_ref of the voltage command is set tov_ref_ave1; an average of an absolute value of the magnitude of thedetected current value i_fb to i_fb_ave1, and the phase of i_fb withrespect to v_ref to θdif1 after the lapse of an arbitrarily set time.

Next, vamp is adjusted to reach a previously set second set currentvalue, and after the lapse of the set time, the average of the absolutevalue of the magnitude v_ref of the current command is set tov_ref_ave2; the average of the absolute value of the magnitude of thedetected current value i_fb to i_fb_ave2; and the phase of i_fb withrespect to v_ref to θdif2 for calculating:Zx={(v_ref_ave2−v_ref_ave1)/√{square root over (3})}/(i _(—) fb_ave2−i_(—) fb_ave1),θdif_(—) L=(θdif1+θdif2)/2Zx _(—) r=Zx·cos θdif_(—) L,Zx _(—) i=Zx·sin θdif_(—) LFrom these, a secondary resistance of the motor is calculated inaccordance with R2=Zx_r−R1, and a leakage inductance in accordance withL=Zx_i/(2·π·fh).

Alternatively, the gains and outputs of the proportional-plus-integralcontrollers, the d-axis auxiliary voltage command and the q-axisauxiliary voltage command are set to zero, and a previously setarbitrary fixed value is set to a voltage phase θv. A magnitude vref ofthe voltage command is given by v_ref=vamp·sin(2·π·f1·t), where f1 is aproper frequency ⅕ or less as high as the rated operation frequency ofthe motor, and vamp is a voltage amplitude. Vamp is incrementally ordecrementally adjusted while monitoring the current value i_fb suchthat:i _(—) fb=√{square root over ((id _(—) fb ² +iq _(—) fb ²))}calculated from a d-axis detected current value id_fb and a q-axisdetected current value iq_fb reaches a previously arbitrarily set firstset current value. After i_fb reaches the first set current value, anaverage of an absolute value of the magnitude v_ref of the voltagecommand is set to v_ref_ave3; an average of an absolute value of themagnitude of the detected current value i_fb to i_fb_ave3; and the phaseof i_fb with respect to v_ref to θdif3 after the lapse of a firstarbitrary set time.

Next, vamp is adjusted to reach a previously set second set currentvalue, and after the lapse of a second arbitrary set time, the averageof the absolute value of the magnitude v_ref of the current command isset to v_ref_ave4; the average of the absolute value of the magnitude ofthe detected current value i_fb to i_fb_ave4; and the phase of i_fb withrespect to v_ref to θdif4 for calculating:Zx2={v_ref_ave4−v_ref_ave3)/√{square root over (3))}/(i _(—) fb_ave4−i_(—) fb_ave3), θdif_(—) m=(θdif3+θdifγ4)/2From these, a mutual inductance of the motor is calculated in accordancewith:

$M = {\frac{R2}{2 \cdot \pi \cdot {f1}} \cdot \sqrt{\frac{{Zx\_ r2} - {R1}}{{R1} + {R2} - {Zx\_ r2}}}}$

The present invention is also directed to an induction motor in a motorcontrol apparatus which is configured to supply a three-phase AC currentto the induction motor through an inverter to operate the motor at avariable velocity, and has a current detector for detecting the currentflowing at two arbitrary phases or three phases of an inverter output; aproportional-plus-integral controller which receives a current commandvalue for a primary current fed to the motor, and a primary currentvalue i_fb of a primary current detector derived from a current valuedetected by the current detector to control an output voltage commandvalue v_ref such that a deviation between both reduces to zero, and apower converter for providing a three-phase AC current based on thevoltage command value v_ref and a voltage output phase θv. The motorcontrol apparatus is configured to convert the motor to an equivalentcircuit of a three-phase Y (star) connection to handle the equivalentcircuit.

The voltage output phase θv is chosen at a previously set arbitraryphase. Prior to applying a current, a current command is fed to operatethe vector control apparatus with a proportional-plus-integralcontroller being set operative. After conduction for a predeterminedtime, a current command value and a detected current value are measured,k is measured at two levels of current, and a primary resistance value(or a line-to-line resistance value) is derived from the slope of thecurrent at that time with the gain of the current controller being setto zero to maintain an integrated value constant and accordingly fix avoltage command value.

Also, the voltage phase θv is chosen at a previously set arbitraryvalue, and the magnitude vref of the voltage command is fed insinusoidal wave. An average of the voltage command value and an averageof the detected current value, as well as a difference in phase betweenthe voltage command value and detected current value are calculatedrespectively at two frequencies. An impedance is determined from thevoltage command value and detected current value, and the impedance isdecomposed into a real component and an imaginary component by the phasedifference. (Primary resistance value+Secondary resistance value) iscalculated from the real component, while the impedance due to a leakageinductance is calculated from the imaginary component. From these, thesecond resistance value and leakage inductance are found.

The present invention is directed to a motor control apparatus whichseparates a primary current of a motor separated into a flux component(d-axis component) and a torque component (q-axis component) for ano-load current value, and has a d-axis currentproportional-plus-integral controller which receives a current commandof the d-axis component and a detected current value of the d-axiscomponent for controlling a deviation between both to reduce to zero,wherein the output of the proportional-plus-integral controller is setto a d-axis voltage command value;

a q-axis current proportional-plus-integral controller which receives acurrent command of the q-axis component and a detected current value ofthe q-axis component for controlling a deviation between both to reduceto zero, wherein the output of the proportional-plus-integral controlleris set to a q-axis voltage command value; and

a power converter for calculating a magnitude v_ref and a voltage phaseθv of a voltage command from the d-axis voltage command value which isan output of the d-axis current proportional-plus-integral controllerand the q-axis voltage command value which is an output of the q-axiscurrent proportional-plus-integral controller, and converting a DCcurrent to a three-phase AC current based on the magnitude of thevoltage command and the phase of the voltage command to provide thethree-phase AC current, wherein the motor control apparatus isconfigured to control the d-axis current command and the q-axis currentcommand to operate the motor in conformity with an arbitrary velocitycommand.

In a normal operating condition, an output frequency fphi, the d-axisvoltage command vd_ref, the q-axis voltage command vq_ref, a d-axisdetected current value id_fb, and a q-axis detected current value iq_fbare measured. Both or one of a mutual inductance M and a no-load currentI0 of the motor is determined using a previously set base voltage v_baseand base frequency f_base of the motor, a primary resistance value R1,and a leakage inductance L.

The present invention is also directed to a motor control apparatusconfigured to supply a three-phase AC current to the induction motorthrough an inverter to operate the motor at a variable velocity, whichhas a power converter for providing the three-phase AC current based onan output voltage command value v_ref and a voltage output phase θv, anda current detector for detecting a primary current flowing into theinduction motor, wherein a detected primary current value i1 derivedfrom a current value detected by the current detector is fed to themotor control apparatus.

An equivalent circuit per phase of the induction motor is created in theform of T-1 type equivalent circuit.

The voltage phase θv is set to a previously set arbitrary fixed value,and a predetermined fixed value to the voltage command value v_ref. Thedetected primary current value i1 flowing into the induction motor atthis time is read, and a current im flowing through a mutual inductanceM is estimated in accordance with:

${\hat{i}m} = {{\left( {1 + \frac{R1}{R2}} \right) \cdot {i1}} - \frac{v\_ ref}{R2}}$using the primary current value i1 and a primary resistance value R1 anda secondary resistance value R2 given by a separate means. A timeconstant {circumflex over (τ)}_(im) is determined from the waveform ofthe estimate îm of the rising current, and the mutual inductance M iscalculated in accordance with:

$M = {\frac{{R1} \cdot {R2}}{{R1} + {R2}} \cdot {\hat{\tau}}_{im}}$

The no-load current I0 is calculated as required, using the mutualinductance M or the time constant {circumflex over (τ)}_(im), theprimary resistance value R1, a leakage inductance L and the secondaryresistance value R2 given by a separate means, and a rated voltage Vrateand a rated frequency frate given as the rating of the motor, and themutual inductance M.

Alternatively, a current im flowing through the mutual inductance M isestimated using the primary current value i1, and a primary resistancevalue R1 and a secondary resistance value R2 given by a separate meansin accordance with:

${\hat{i}m} = {{i1} - {\frac{R1}{R2}\left( {{i1}_{co} - {i1}} \right)}}$without using a voltage value, where i1 represents a constant value towhich the primary current value i1 converges when the voltage commandv_ref is applied.

According to the present invention it is possible to accurately tune theprimary resistance and secondary resistance, a leakage inductance and amutual inductance or a no load current, which are required foraccurately controlling an induction motor, even when a load is coupledto the induction motor.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an induction motor control apparatusaccording to one embodiment of the present invention;

FIG. 2 is a configuration diagram of average/phase difference calculator8;

FIG. 3 is a T-1 type equivalent circuit diagram of an induction motor;

FIG. 4 is an equivalent circuit diagram during primary resistancetuning;

FIG. 5 is a time chart of a voltage command value and a detected currentvalue during the primary resistance tuning;

FIG. 6 is a graph of the voltage command value and detected currentvalue during the primary resistance tuning;

FIG. 7 is an equivalent circuit diagram during secondary resistance andleakage inductance tuning;

FIG. 8 is a vector diagram of an impedance in the equivalent circuitduring the secondary resistance and leakage inductance tuning;

FIG. 9 is a time chart of a voltage command value and a detected currentvalue during the secondary resistance and leakage inductance tuning;

FIG. 10 is a block diagram when a tenth embodiment is applied;

FIG. 11 is a block diagram when eleventh to thirteenth and seventeenthembodiments are applied;

FIG. 12 is a T-1 type equivalent circuit diagram of an induction motor;

FIG. 13 is an equivalent circuit diagram when a DC current is fed to theinduction motor;

FIG. 14 is a time chart of a voltage command value and a detectedcurrent value during primary resistance tuning;

FIG. 15 is a graph of the voltage command value and detected currentvalue during the primary resistance tuning;

FIG. 16 is a block diagram when a fourteenth and a fifteenth embodimentare applied;

FIG. 17 is a configuration diagram of average/phase differencecalculator 8;

FIG. 18 is an equivalent circuit during secondary resistance and leakageinductance tuning;

FIG. 19 is a time chart of a voltage command value and a detectedcurrent value during the secondary resistance and leakage inductancetuning;

FIG. 20 is a vector diagram of an impedance in the equivalent circuitduring the secondary resistance and leakage inductance tuning;

FIG. 21 is a diagram showing a change due to the frequency of a realcomponent of the impedance in the equivalent circuit during thesecondary resistance and leakage inductance tuning;

FIG. 22( a) is a diagram showing the relationship between a current anda voltage value when signals at 15 Hz is applied, and FIG. 22( b) is adiagram showing the relationship between a current and a voltage valuewhen signals at 30 Hz is applied;

FIG. 23 is a block diagram when a sixteenth to a nineteenth embodimentare applied;

FIG. 24 is a T-1 type equivalent circuit diagram of an induction motor;and

FIG. 25 is a diagram showing a time-varying waveform of a current whenthe induction motor is applied with a DC voltage.

BEST MODE FOR CARRYING OUT THE INVENTION

FIG. 1 is a block diagram illustrating the configuration of oneembodiment of an induction motor control apparatus in the presentinvention. Proportional-plus-integral controller 10 performs a controlsuch that a deviation between q-axis current command iq_ref and detectedq_axis current value iq_fb becomes zero, and q-axis auxiliary voltagecommand vq_ref_c is added to the output of proportional-plus-integralcontroller 10 to create q-axis voltage command vq_ref. Similarly,proportional-plus-integral controller 11 performs a control such that adeviation between d-axis current command id_ref and detected d-axiscurrent value id_fb becomes zero, and d-axis auxiliary voltage commandvd_ref_c is added to the output of proportion integration controller 11to create d-axis voltage command vd_ref. A proportional gain of aproportional integrator is represented by Ki, and an integral gain by(1/T). Voltage command processor 12 calculates magnitude v_ref andvoltage phase θv of a voltage command from vq_ref and vd_ref, and alsoadds phase θphi of magnetic flux to θv to calculate a voltage phase onthree-phase AC coordinates. Also, voltage command offset value v_ref_ofsis added to the magnitude v_ref of the voltage command. Here, iq_ref,id_ref and fphi are given by separately provided calculation circuitsduring a normal operating condition of an induction motor. Powerconverter 2 serves to supply induction motor 3 with a three-phase ACvoltage based on the above-mentioned v_ref+v_ref_ofs and θref. Currentsflowing into induction motor 3 are detected by current detectors 4 and5, and fed to coordinate converter 6 where they are converted to iq_fband id_fb on d_q coordinates. iq_fb and id_fb are converted to magnitudei_fb of their composite vector by current processor 7. Average and phasedifference calculator 8 is a calculator for calculating averages of thevoltage command and detected current value as well as a phase differencebetween the voltage command and detected current value, which arerequired for calculating a motor constant of induction motor 3, fromv_ref+v_ref_ofs and i_fb. Motor constant processor 1 is a calculator forcalculating the motor constant of induction motor 3 based on signalscalculated by average and phase difference calculator 8.

FIG. 2 illustrates the specific configuration of average and phasedifference calculator 8, that calculates, from v_ref_out and i_fb, aphase difference between them, averages of absolute values of respectivefrequency components, and DC components. Here, the average is derivedthrough a low pass filter (LPF), but may be calculated in accordancewith a method based on moving average or the like.

FIG. 3 illustrates a T-1 type equivalent circuit of an induction motorwhich is used for determining a motor constant of the induction motor inthis embodiment. FIG. 3 is an equivalent circuit for each phase, and isapplied with a voltage expressed by:v_ref/√{square root over (3)}I1 is a primary current of the motor; R1 is a primary resistance of themotor; R2 is a secondary resistance of the motor; 1 is a leakageinductance of the motor; and M is a mutual inductance of the motor.

A first embodiment will be described.

When a DC current is applied to induction motor 3, impedance ωM atmutual inductance M is zero, so that the equivalent circuit in FIG. 3 ischanged as illustrated in FIG. 4. Therefore, primary resistance R1 iscalculated in accordance with:R1=(v_ref/√{square root over (3))}/I1

When setting as a line-to-line resistance, RL-L=2·R1 is handled as theline-to-line resistance. As tuning is started for the primaryresistance, iq_ref and id_ref are applied as primary current commandvalues arbitrarily set as a current command. As the current command isgiven, a voltage command is generated in accordance with the gain ofproportional-plus-integral controllers 10, 11, and a three-phase ACvoltage is delivered from power converter 2 and applied to motor 3through which current I1 flows. Current I1 is detected by currentdetectors 4, 5, subjected to coordinate conversion and currentprocessing, and resulting i_fb is applied to motor constant processor 1.A time required for the current to rise is determined by the gain ofproportional-plus-integral controllers 10, 11, so that this time is setas a previously set arbitrary time, and the proportional gain of theq-axis and d-axis proportional-plus-integral controllers is set to zeroafter the lapse of the set time. Since this causes zero to be fed to theintegrator, the output of the proportional controller is fixed to anoutput value immediately before the proportional gain is set to zero,thereby stably maintaining the voltage command at a fixed value. Waitinga constant time in this state, averages are measured for voltage commandv_ref and detected current value i_fb during the time, and are set tov_ref1 and i_fb1, respectively. Next, the proportional gain ofproportional-plus-integral controllers 10, 11 is returned to an originalvalue, and current command values iq_ref ad id_ref are used as secondset current values, and are manipulated in a similar manner. Averages ofthe voltage command values and current command values at this time areset to v_ref2, i_fb2, respectively. A change over time in voltagecommand v_ref and detected current value i_fb in this event are shown inFIG. 5. The relationship between v_ref1, i_fb1, v_ref2, i_fb2 isestablished as shown in FIG. 6, wherein primary resistance value R1 isdetermined from the slope of this linear line. Considering that v_ref isa line-to-line value, R1 is given by:R1={(v_ref2−v_ref1)/√{square root over (3)}}/(i _(—) fb2−i _(—) fb1)

A second embodiment will be described.

The present embodiment is a modification of the first embodimentdescribed above, wherein when proportional gain Ki ofproportional-plus-integral controllers 10, 11 is set to zero, the q-axisand d-axis voltage commands at that time are substituted into auxiliaryvoltage command values vq_ref_c and vd_ref_c, respectively, andsimultaneously, proportional gain Ki and integral gain (1/T) ofproportional-plus-integral controllers 10, 11, and the outputs ofproportional-plus-integral controllers 10, 11 are set to zero, such thata resulting voltage command is applied. The remaining processing is thesame as the first embodiment.

A third embodiment will be described.

While the current level is measured at two points in the first andsecond embodiments described above, the measurements are made at threepoints or more for improving the measurement accuracy in thisembodiment. Describing for measurements at three points, whenmeasurements are made at points 1, 2, 3, R1 is calculated in intervalsbetween points 1 and 2, between points 2 and 3, and between points 1 and3, respectively, or in arbitrary two of these intervals, as is the casein the first and second embodiments, and an average of calculated valuesis employed as R1 which should be determined. For measurements at fourpoints or more, R1 may be similarly calculated in arbitrary intervals,such that an average of calculated values is used.

A fourth embodiment will be described.

The voltage command is given as v_ref=vamp·sin(2·π·fh·t), and θref as anarbitrary fixed value. Vamp is initially set to zero, and fh is set to avalue equal to or higher than the rated operation frequency of themotor. When the frequency is high, an equivalent circuit becomes asillustrated in FIG. 7 on the assumption that a current hardly flows intoM because ωM>>R2 stands in the equivalent circuit illustrated in FIG. 3.When the phase difference between the voltage and current at this timeis represented by θdif, the relationship between (R1+R2) and ω1 isestablished as shown in FIG. 8, represented by (R1+R2)=|Zx|·cos θdif,and ω1=|Zx|·sin θdif, where |Zx| indicates the impedance of the circuit.Thus, R2 and L can be derived using previously determined R1.

For determining |Zx|, v_ref shown above is applied, and vamp isgradually increased until average i_fb_ave of the absolute value of thedetected current value reaches a previously set first set current value.When i_fb_ave matches the set value, average v_ref_ave of the absolutevalue of a frequency component of v_ref, average i_fb_ave of theabsolute value of the detected current value, and phase difference θdifare stored in a memory as v_ref_ave1, i_fb_ave1, θdif1, respectively,after waiting for a certain time until the output of the filter becomesstable. Next, vamp is adjusted such that average i_fb_ave reaches apreviously set second set current value, and the value is similarly readwhen i_fb_ave matches the second set current value. Then, averagev_ref_ave, average i_fb_ave and phase difference θdif are stored asv_ref_ave2, i_fb_ave2, θdif2, respectively. FIG. 9 shows a change overtime in the voltage command and detected current value in this case.Impedance |Zx| of the circuit is calculated in accordance with:|Zx|={(v_ref_ave2−v_ref_ave1)/√{square root over (3)}}/(i _(—) fb_ave2−i_(—) fb_ave1)as the slope of the voltage and current, as in the case of R1.

The phase difference is calculated in accordance withθdif_L=(θdif1+θdif2)/2.

From this equation and the aforementioned equation, secondary resistanceR2 and leakage inductance L are calculated in accordance with:R2={(v_ref_(—ave)2−v_ref_ave1)/√{square root over (3)}}/(i _(—)fb_ave2−i _(—) fb_ave1)·cos θdif_(—) L−R1,L=[{(v_ref_ave2−v_ref_ave1)/√{square root over (3)}}/(i _(—) fb_ave2−i_(—) fb_ave1)·sin θdif_(—) L]/(2·π·fh)

While the explanation has been made with the initial value for vampbeing zero, the value of a flowing current can be predicted withreference to a V/f pattern, so that a reduction in time can be made bypreviously setting some value and increasing or decreasing from thisvalue.

A fifth embodiment will be described.

The present embodiment is a modification of the fourth embodiment,wherein v_ref_ofs is added to voltage command v_ref as an offset value,and the resulting value is used as a voltage command. As illustrated inFIG. 2, data v_ref_ave, i_fb_ave, θdif for use in calculating R1+R2 andL can be handled in a similar manner to the fourth embodiment by usingdata from which a DC component is removed by passing an input signalthrough a high pass filter.

A sixth embodiment of the invention will be described.

The present embodiment is a modification of the fourth embodiment,wherein v_ref_ofs is added to voltage command v_ref as an offset value,and the resulting value is used as a voltage command. Since the voltageequivalent to the offset value is provided as a DC component, anequivalent circuit therefor is that illustrated in FIG. 4, so thatprimary resistance R1 is determined by calculating the ratio of a DCcomponent of this voltage command value to a DC component of thedetected current value. To extract a DC component of a signal, thesignal may be averaged. In the embodiment, a low pass filter [LPF3] isused for detection as illustrated in FIG. 2. The value of v_ref_ofs isdetermined herein by adjusting v_ref_ofs, while comparing the detectedcurrent value with the set current value in a manner similar to thefourth embodiment, before an AC signal is applied.

The sixth embodiment is the same as the fourth embodiment except that R1thus determined is used for calculating R2. In this way, since R1, R2, Lcan be determined in a single step, the execution time can be reduced.

A seventh embodiment of the invention will be described.

In the fourth embodiment, frequency f1 is set at a very low frequencywith respect to the rated operation frequency of the motor. In thisevent, since a current flowing into M cannot be ignored, the equivalentcircuit illustrated in FIG. 3 is based on the following discussion.

The equivalent circuit is expressed by the equation:

${{\left( {{R1} + {{j\omega}\; L} + \frac{{j\omega}\;{MR2}}{{R2} + {{j\omega}\; M}}} \right){I1}} = {{v\_ ref}/\sqrt{3}}},{\omega = {2 \cdot \pi \cdot {fh}}}$This equation is solved to derive:

${\frac{{R1R2}^{2} + {\omega^{2}M^{2}{R1}} + {\omega^{2}M^{2}{R2}}}{{R2}^{2} + {\omega^{2}M^{2}}} + {j\frac{{\omega\;{LR2}^{2}} + {\omega^{3}{LM}^{2\prime}} + {\omega\;{MR2}}}{{R2}^{2} + {\omega^{2}M^{2}}}}} = {\frac{{v\_ ref}/\sqrt{3}}{I1} = {{Zr} + {j\;{Zi}}}}$where:

${{Zr} = {{\frac{{v\_ ref}/\sqrt{3}}{I1} \cdot \cos}\;\theta\; m}},{{Zi} = {{\frac{{v\_ ref}/\sqrt{3}}{I1} \cdot \sin}\;\theta\; m}},{{\theta\; m} = {\tan^{- 1}\left( \frac{{\omega\;{LR2}^{2}} + {\omega^{3}{LM}^{2}} + {\omega\;{MR2}}}{{R1R2}^{2} + {\omega^{2}M^{2}{R1}} + {\omega^{2}M^{2}{R2}}} \right)}}$M is calculated by comparing real parts:

$M = {\frac{R2}{\omega} \cdot \sqrt{\frac{{Zr} - {R1}}{{R1} + {R2} - {Zr}}}}$Thus, M is derived.

Here, when M is calculated in a similar manner to the fourth embodimentexcept that fh is set at a low frequency, and the impedance isrepresented by |Zx2| and the phase difference by θdif_m,Zx _(—) r2=|Zx2|·cos θdif_(—) m

From this and previously determined R1, R2, mutual inductance M iscalculated in accordance with:

$M = {\frac{R2}{2 \cdot \pi \cdot {f1}} \cdot \sqrt{\frac{{Zx\_ r2} - {R1}}{{R1} + {R2} - {Zx\_ r2}}}}$

Eighth and ninth embodiments will be described.

In the present embodiment, similar to those shown in the fifth and sixthembodiments, v_ref_ofs is added to voltage command v_ref as an offset.Details on the processing are the same as those shown in the fifth andsixth embodiments. Since the frequency is low in the seventh embodiment,the motor can be prevented from unnecessarily moving by applying a DCoffset, as shown in this method.

A tenth embodiment will be described.

FIG. 10 illustrates a block diagram in which a tenth embodiment of theinvention is implemented. From a configuration for conducting a normalvector control, q-axis voltage command value vq_ref, d-axis voltagecommand value vd_ref, q-axis detected current value iq_fb, d-axisdetected current value id_fb and output frequency value fphi areextracted and fed to motor constant culculator 1 to calculate mutualinductance M and no-load current value I0. Velocity controller 14calculates q-axis current command value iq_ref, d-axis current commandvalue id_ref and output frequency value fphi based on a velocity commandin accordance with a generally used vector control scheme. Velocitycontroller 14 is simplified for description since it does not relate tothe features of the present invention. Coordinate converter 6 is acoordinate converter for converting a detected phase current value to avalue in a dq-coordinate system. q-axis PI current controller 10 andd-axis PI current controller 11 are controllers for controlling thecurrent command value to match the detected current value. Voltagecommand calculator 12 calculates magnitude v_ref and voltage phase θv ofa three-phase AC voltage from the q-axis voltage command, d-axis voltagecommand value, and magnetic flux phase θphi. Magnetic flux phase θphi iscalculated by integrating output frequency fphi. Power converter 2supplies three-phase AC power to induction motor 3 based on v_ref andθv.

Here, after an operation command is fed, output frequency fphi, d-axisvoltage command vd_ref, q-axis voltage command vq_ref, d-axis detectedcurrent value id_fb, and q-axis detected current value iq_fb are readafter the lapse of one second from the time an acceleration of inductionmotor 3 is completed, and the following equations:

$\begin{matrix}{{Vqq} = {\frac{vq\_ ref}{\sqrt{3}} - {{R1} \cdot {iq\_ fb}} - {2{\pi \cdot {fphi} \cdot L \cdot {id\_ fb}}}}} \\{{Vqq} = {\frac{vd\_ ref}{\sqrt{3}} - {{R1} \cdot {id\_ fb}} - {2{\pi \cdot {fphi} \cdot L \cdot {iq\_ fb}}}}} \\{Q = {{{Vqq} \cdot {id\_ fb}} - {{Vqq} \cdot {iq\_ Fb}}}} \\{E = \sqrt{{Vqq}^{2} + {Vdd}^{2}}} \\{M = \frac{E^{2}}{2{\pi \cdot {fphi} \cdot Q}}} \\{{I0} = \frac{{v\_ base}/\sqrt{3}}{2{\pi \cdot {f\_ base}}\left( {M + L} \right)}}\end{matrix}$are calculated using previously set base voltage v_base and basefrequency f_base of the motor, and separately calculated primaryresistance value R1 and leakage inductance L to determine mutualinductance M and no-load current I0 of the motor.

While it is assumed the measurements are made upon completion of theacceleration, the measurement may be made at any arbitrary time duringoperation.

The method according to the present invention extracts signals from therespective components for calculations in a normal operating condition,and can therefore be applied irrespective of a difference inconfiguration of the velocity controller due to the presence or absenceof PG (Pulse Generator) and the like.

FIG. 11 is a block diagram illustrating the configuration of a motorcontrol apparatus which implements the method of measuring a motorconstant for an induction motor in the eleventh to thirteenthembodiments. Motor constant calculator 1 delivers current command i_ref.The values of currents flowing into induction motor 3 are captured ascurrent iu detected by current detector 4 for U-phase and current ivdetected by current detector 5 for v-phase. Three-phase/two-phaseconverter 6 performs calculations expressed by Equations (1) and (2) toconvert iu and iv to two-phase AC currents iα and iβ.iw=−(iu+iw)  (1)

$\begin{matrix}{\begin{bmatrix}{i\alpha} \\{i\beta}\end{bmatrix} = {{\frac{2}{3}\begin{bmatrix}{1 - \frac{1}{2} - \frac{1}{2}} \\{0 - \frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2}}\end{bmatrix}}\begin{bmatrix}{iu} \\{iv} \\{iw}\end{bmatrix}}} & (2)\end{matrix}$

The phases at which currents are detected are not limited to acombination of U-phase and v-phase, but the current may be detected attwo arbitrary phases or at all the three phases.

Current calculator 7 calculates a square root of the sum of squaredtwo-phase AC currents iα, iβ to find detected current value i_fb. i_fbis fed to average and phase difference calculator 8 to calculate averagei_fb_ave. While the average is herein calculated by taking the absolutevalue of i_fb and passing the result through a low pass filter, anothermethod such as moving average may be used to calculate the average.Current Proportional-plus-integration controller 13 performs a controlsuch that current command i_ref matches average detected current valuei_fb_ave. The output of current Proportional-plus-integration controller13 is voltage command v_ref. Power converter 2 converts voltage commandvalue v_ref into a line-to-line voltage, calculates the output phase ofa three-phase AC current using voltage phase θv applied from motorconstant calculator 1, and supplies induction motor 3 with three-phaseAC power.

An eleventh embodiment will be described.

FIG. 12 illustrates a T-1 type equivalent circuit for one phase of aninduction motor. R1 represents a primary resistance; L a leakageinductance; M a mutual inductance; R2 a secondary resistance; and s aslippage. When a DC current is fed, an impedance component of mutualinductance M is zero, so that the equivalent circuit is changed asillustrated in FIG. 13.

The following description will be made on the assumption that the phaseis at 0° when a current at U-phase reaches a peak.

In this embodiment, voltage phase θv is at 0°.

First, when a value equal to 20% of the rated current of the inductionmotor is applied as current command value i_ref, voltage command v_refis changed as shown in FIG. 14 by the action of currentProportional-plus-integration controller 13. At the time detectedcurrent value i_fb_ave matches i_ref1, v-ref becomes constant. Here, thewidth of section A for controlling the current over time is determinedby waiting for two seconds. Since the time until the stability isensured is related to control characteristics, a wait for two seconds isgenerally sufficient. However, if the gain of currentProportional-plus-integration controller 13 cannot be increased due tothe characteristics of a load machine or the like, this time should beextended. After the lapse of two seconds, gain Ki of currentProportional-plus-integration controller 13 is set to zero, and thevalue saved in the integrator is delivered as v_ref, thereby fixingcurrent command value v_ref. After waiting a certain time (here, onesecond), v_ref_ave which is an average of v_ref, and i_fb_ave which isan average of i_fb are read, and set to v_ref1, i_fb1, respectively,v_ref_ave is calculated by feeding the value of v_ref to average andphase difference calculator 8. Next, 40% of the rated current of theinduction motor is applied as current command i_ref, and a similarcontrol is conducted. Then, voltage command value v_ref_ave and detectedcurrent value i_fb_ave are read, and set to v_ref2, i_fb2, respectively.The data at two points are plotted as shown in FIG. 15. Since this sloperepresents primary resistance value R1, R1 is calculated in accordancewith:R1={(v_ref2−v_ref1)/√{square root over (3)}}/(i _(—) fb2−i _(—) fb1)

Then, 2×R1 is set to line-to-line resistance value RL-L. While thecurrent value is set herein to 20% and 40% of the rated current of theinduction motor, different values may be used, or the foregoingoperation may be performed at three points or more of the current value.

In the twelfth embodiment, measurements at three points or more aremade. When the measurements are made, for example, at three points ofcurrent values 20%, 40%, 60%, the slopes are calculated respectivelybetween 20% and 40%, between 40% and 60% and between 20% and 60%. Theslopes may be averaged for use.

A thirteenth embodiment will be described. As shown in FIG. 15, thepreviously measured data is approximated by a linear function andextended for recording the value of v_ref when the current value iszero, as voltage offset value v_ref0. This corresponds to a voltage dropcaused by devices used for power converter 2 and the like. When themeasurements are made at three points or more of the current value, thevoltage offset value may be found by linear approximation of twoarbitrary points or a regression curve based on a mean square errormethod.

A fourteenth embodiment will be described. FIGS. 16 and 17 are blockdiagrams for implementing methods of a fourteenth embodiment and afifteenth embodiment.

In FIG. 15, output voltage command v_ref and output voltage phase θv areapplied from motor constant calculator 1 to power converter 2 to supplya three-phase AC current based thereon for operating induction motor 3.The value of the current flowing into induction motor 3 is captured ascurrent iu detected by current detector 4 for U-phase and current ivdetected by current detector 5 for v-phase. Coordinate converter 6performs the calculations expressed by Equations (1) and (2) to convertiu and iv to two-phase AC currents iα and iβ. The phases at which thecurrents are detected are not limited to a combination of U-phase andv-phase, but the current may be detected at two arbitrary phases or atall the three phases.

Current calculator 7 calculates a square root of the sum of squaredtwo-phase AC currents iα, iβ to find detected current value i_fb.Voltage command v_ref, detected current value i_fb, and phase θh atwhich an instantaneous value of the amplitude is given for v_ref appliedby motor constant calculator 1, are fed to average and phase differenceprocessor 8 which calculates v_ref_ave which is an average of v_ref,i_fb_ave which is an average of i_fb, and phase difference θdif whichare fed to motor constant calculator 1 for calculating a motor constant.Differences of FIG. 15 from FIG. 11 are that voltage command v_ref isapplied instead of the current command, and average and phase differencecalculating circuit 8 is applied with phase θh of a frequency componentwhich is given as voltage command v_ref. FIG. 17 is a block diagramillustrating the configuration of average and phase differencecalculator 6. Average and phase difference processor 6 calculates v_ref,i_fb_ave which is an average of i_ref, and phase difference θdif basedon the processing in the block diagram of FIG. 17.

The equivalent circuit of the induction motor illustrated in FIG. 12 canbe approximated to a series circuit of R1, L, R2 as illustrated in FIG.18 because impedance ωM by mutual inductance M becomes larger ascompared with R2 at higher frequencies. Therefore, resistance componentR1+R2 and reactance component ωL are determined from the magnitudes ofthe voltage and current, and the phase difference between them.

In this embodiment, θv is set to 0°; first frequency fh1 to 15 Hz;second frequency fh2 to 30 Hz; and the set current value described inthe fourteenth embodiment to 80% of the rated current of the inductionmotor. First, the induction motor is operated with the magnitude of thevoltage amplitude Vamp set to zero, and the magnitude of the voltagecommand given by v_ref=vamp·sin(2·π·15·t), where t is time. Voltageamplitude Vamp is adjusted while i_fb is monitored such that averagedetected current value i_fb reaches 80% of the rated current of theinduction motor. Vamp should be adjusted by an appropriate step whichdoes not cause the current to suddenly change. In this embodiment, astep equal to 1/1000 of the rated voltage of the induction motor wasadded to or subtracted from Vamp. After average detected current valuei_fb reaches 80% of the rated current of the induction motor, an averageof the absolute value of magnitude v_ref of the voltage command is setto v_ref_ave1; an average of the absolute value of the magnitude ofdetected current value i_fb to i_fb_ave1; and the phase of i_fb withrespect to v_ref to θdif1 after the lapse of an arbitrarily set time(here three seconds). Next, the frequency is set to 30 Hz at which asimilar operation is performed to that at 15 Hz. In this event, anaverage of the absolute value of magnitude v_ref of the voltage commandis set to v_ref_ave2; an average of the absolute value of the magnitudeof detected current value i_fb to i_fb_ave2; and the phase of i_fb withrespect to v_ref to θdif2. Here, respective saturated values are fed tolow pass filters, the outputs of which are used for the averages. A timechart of the voltage command and detected current value at this time isshown in FIG. 19. When the relationship between the voltage, current andphase difference established herein is handled in complex numbers asshown in FIG. 20, the impedance, and its real component and imaginarycomponent are given by the following equations:Zx1=(v_ref_ave1/√{square root over (3)})/(i _(—)fb_ave1),Zx2=(v_ref_ave2/√{square root over (3)})/(i _(—) fb_ave2)Zxr1=Zx1·cos θdif_(—)1, Zxr2=Zx2·cos θdif_(—)2,Zxi1=Zx1·sin θdif_(—)1, Zxi2=Zx2·sin θdif_(—)2,

In this event, real components Zxr1, Zxr2 represent resistance componentR1+R2, while imaginary components Zxi1, Zxi2 represent reactancecomponent ωL. First, consider the real components. Zxr1 at fh1 (15 Hz)and Zxr2 at fh2 (30 Hz) are graphically represented as shown in FIG. 21,and change together with the frequency. This is presumably due to theinfluence of a skin effect and the like. R2 is calculated in accordancewith R2=Zxr−R1, whereas R1 is measured by feeding a DC current, so thata value when frequency fh is at 10 Hz(fh=fh1·fh2/(fh1+fh2)=15·30/(15+30)) is as Zxr through linearapproximation of measured values as shown in FIG. 21. Next, consider theimaginary components. Since the imaginary components are substantiallyproportional to the frequency component, the leakage inductance iscalculated in accordance with L=Zxi/(2·π·fh_(—)1) using the values atfh2 (30 Hz), where Zxi=Zxi2 and fh_(—)1=fh2. Here, fh2 is used becausethe voltage value becomes larger at a higher frequency, resulting in areduction in measurement error. The lower frequency may be used, or theleakage inductance may be calculated from the slope at two frequencies.

Next, a fifteenth embodiment will be described. In the measurement ofthe secondary resistance and leakage inductance, the previouslydetermined voltage offset value v_ref0 is used to calculate Zx1 and Zx2by the following equations:Zx1=(v_ref_ave1/√{square root over (3)}−v_ref0)/(i _(—) fb_ave1),Zx2=(v_ref_ave2/√{square root over (3)}−v_ref0)/(i _(—) fb_ave2)

The subsequent calculations are similar to the foregoing.

In the fourteenth embodiment, similar measurements are made at the samefrequency as the foregoing and with application of current i_fb2different in magnitude from the current value fed during themeasurement. Here, as an example, i_fb2 is set to 40% of the ratedcurrent of the motor (one half of the foregoing), and an average of theabsolute value of the voltage command value at 15 Hz is set tov_ref_ave3; an average of the absolute value of the detected currentvalue at 15 Hz to i_fb_ave3; and an average of the voltage command valueat 30 Hz to v_ref_ave4; and an average of the absolute value of thedetected current value at 30 Hz to i_fb_ave4. As shown in FIGS. 22( a),22(b), linear approximation is made with two current values at 15 Hz, 30Hz, respectively, and the values at the current value equal to zero arederived as voltage offset v_ofs15 at 15 Hz and voltage offset v_ofs30 at30 Hz. In another method, these offset values may be used for thevoltage command values at 15 Hz, 30 Hz instead of voltage offset valuev_ref0 in the thirteenth embodiment to compensate for the voltageoffset. Alternatively, rather than deriving the voltage offset values,the impedances may be calculated at 15 Hz, 30 Hz, respectively, from theslope when the current value is changed. Also, an average value of twocurrent values may be used for the phase to calculate a real part and animaginary part of the impedance.

Though description has been omitted in the foregoing processing forsimplification, the voltage values and current values when the signalsat 15 Hz, 30 Hz are applied are passed through low pass filters foraveraging, after their absolute values are taken, and therefore they areaverages. On the other hand, voltage value offset value v_ref0 describedin a thirteenth embodiment is derived from a DC value and therefore isan effective value or a maximum value, so that v_ref0 is converted to anaverage which is used. While the average is used herein, any of theeffective value, average, maximum value may be used as long as theconversion associated therewith is consistent.

FIG. 23 is a block diagram illustrating the configuration of anapparatus for implementing a method of measuring a motor constant for aninduction motor in a sixteenth and a seventeenth embodiment of thepresent invention. In FIG. 23, power converter 2 converts voltagecommand v_ref and voltage phase θv applied from motor constantcalculator 1 to three-phase AC power which is supplied to inductionmotor 3. The values of currents flowing into induction motor 3 arecaptured as current iu detected by current detector 4 for U-phase andcurrent iv detected by current detector 5 for v-phase. Coordinateconverter 6 performs the calculations expressed by Equations (1) and (2)to convert iu and iv to two-phase AC currents iα and iβ.

In Equation (2), the multiplication by (2/3) is intended for equalingthe magnitude of the amplitude before and after the conversion. Thephases at which the currents are detected are not limited to acombination of the U-phase and v-phase, but the currents may be detectedat arbitrary two phases or at all the three phases. Two-phase ACcurrents iα and iβ are fed to motor constant calculator 1 whichcalculates detected primary current value i1 as a square root of the sumof squared two-phase AC currents iα, iβ.

FIG. 23 shows an inverter-based motor driving apparatus from which partsrequired for practicing the present invention are extracted, whereinblocks such as velocity control, current control and the like disposedprior to voltage command and output voltage phase are replaced by motorconstant calculator 1 during a normal operation in a conventional methodof identifying a motor constant. Both are switched by an additionalswitch.

First, description will be made on the principle of a sixteenthembodiment.

FIG. 24 illustrates a T-1 type equivalent circuit per phase in aninoperative induction motor (slippage s=1). R1 represents a primaryresistance; L a leakage inductance; R2 a secondary resistance; M amutual inductance; v an applied voltage; i1 a primary current of themotor; i2 a secondary current of the motor; and im a current (excitedcurrent) flowing through mutual inductance M.

When an electromotive force generated by a change in the current flowingthrough mutual conductance M is represented by em, equations based onKirchhoff's law are established in the equivalent circuit of FIG. 24 asfollows:

$\begin{matrix}{v = {{{R1} \cdot {i1}} + {L\frac{\mathbb{d}{i1}}{\mathbb{d}l}} + e_{m}}} & (3) \\{e_{m} = {{M\frac{\mathbb{d}{im}}{\mathbb{d}l}} = {{R2} \cdot {i2}}}} & (4)\end{matrix}$i1=im+i2  (5)

Since leakage inductance L is smaller than mutual inductance M, Equation(3) is transformed into:v=R1·i1+e _(m)  (6)when leakage inductance L is ignored for simplification.

Also, from Equations (4) and (5):

$\begin{matrix}{{i1} = {{im} + {\frac{1}{R2} \cdot M \cdot \frac{\mathbb{d}{im}}{\mathbb{d}l}}}} & (7)\end{matrix}$

Equations (4) and (7) are substituted into Equation (6) for integration:

$\begin{matrix}{v = {{{R1} \cdot {im}} + {\frac{M\left( {{R1} + {R2}} \right)}{R2} \cdot \frac{\mathbb{d}{im}}{\mathbb{d}l}}}} & (8)\end{matrix}$

when Equation (8) is solved for im with an initial condition of:im0=0 when t=0  (9)

$\begin{matrix}{{im} = {\frac{v}{R1} \cdot \left( {1 - e^{- \frac{1}{\tau}}} \right)}} & (10) \\{\tau = {- \frac{M\left( {{R1} + {R2}} \right)}{{R1} \cdot {R2}}}} & (11)\end{matrix}$where τ is a time constant.

Thus,

$\begin{matrix}{M = {\frac{{R1} \cdot {R2}}{{R1} + {R2}} \cdot \tau}} & (12)\end{matrix}$is established. As time constant τ is determined from current im flowingthrough mutual inductance M and substituted into Equation (12), mutualconductance M can be calculated.

Description will be made on the principle of a seventeenth embodiment.

Current im flowing through mutual inductance M is a current which flowswithin the induction motor, so that it cannot be directly measured fromthe input terminal of the induction motor. Therefore, description willbe next made on a method of estimating current im flowing through mutualinductance M.

From Equations (4) and (6):

$\begin{matrix}{{i2} = \frac{v - {{R1} \cdot {i1}}}{R2}} & (13)\end{matrix}$

Substituting Equation (13) into Equation (5):

$\begin{matrix}{{im} = {{{i1} - {i2}} = {{i1} - \frac{v - {{R1} \cdot {i1}}}{R2}}}} & (14)\end{matrix}$

Rearrangement of Equation (14) results in:

$\begin{matrix}{{im} = {{\left( {1 + \frac{R1}{R2}} \right) \cdot {i1}} - \frac{v}{R2}}} & (15)\end{matrix}$

In this way, im can be calculated in accordance with Equation (15) usingvoltage v applied to the motor, and primary current i1 flowing into themotor. Then, time constant τ is determined from a change in this im, andsubstituted into Equation (12), whereby mutual inductance M can becalculated.

No-load current I0 is a current which flows when the induction motor isapplied with the power at the rated voltage and rated frequency androtated without load, in which case an equivalent circuit is representedby a series circuit of R1, L, M in the form of T-1 type equivalentcircuit in FIG. 24.

Therefore, the relationship between voltage v and current i1 in thisevent is expressed by:v=R1·i1+jω(L+M)·i1  (16)ω=2πf, where f is the frequency of the power  (17)

Equation (16) is rewritten only with attention paid to the magnitudes ofthe voltage and current to derive the rated voltage V:V=√{square root over (R1 ² +ω ² (L+M) ² )}·I0  (18)

V, I are values indicative of the magnitudes of the voltage and current,respectively, and may be any of effective values, maximum values oraverages as long as the same one is employed for the voltage andcurrent.

When Equation (18) is solved for I0:

$\begin{matrix}{{I0} = \frac{v}{\sqrt{{R1}^{2} + {\omega^{2}\left( {L + M} \right)}^{2}}}} & (19)\end{matrix}$no-load current I0 is calculated.

Although R1 and L are taken into consideration in Equations (16), (18),(19), R1 and L may be ignored for simplification.

FIG. 25 shows the waveform of a change over time of estimate îm of imcalculated in accordance with Equation (15) using primary current i1when voltage v equal to V1 is applied stepwise, current im flowingthrough mutual inductance, primary current i1, and R1, R2. I1_(∞) towhich i1, im, îm converge is (V1/R1), and the waveform of îm changingfrom 0 to i1_(∞) can be confirmed to substantially match the waveform ofim. Therefore, time constant {circumflex over (τ)}m may be determinedfrom a change in îm at this time.

Now, contents of a method implemented on the basis of the foregoingprinciple will be described with reference to FIG. 23.

The following description will be made on the assumption that thecurrent at the U-phase reaches a peak at phase of 0°.

In this embodiment, voltage phase θv was set at 0° for implementation.

First, description will be made on a method of determining the magnitudeof predetermined voltage V1 applied to motor 3. While voltage V1 appliedto motor 3 may be at an arbitrary value, voltage V1 must actually belimited within a range in which induction motor 3 is not damaged by heatgenerated by the current. Therefore, description on the method ofdetermining V1 will be made herein in an example in which voltage V1 isapplied such that a resulting current value reaches 50% of the ratedcurrent of the motor. First, voltage command v_ref at zero is applied,and v_ref is increased in increments of 1/1000 of the rated voltage ofthe induction motor while detected current value i1 is measured. Then,at the time detected current value i1 reaches 50% of the rated currentof the induction motor, the value of v_ref at this time is stored as V1,and the power supplied to motor 3 is shut off. The increment for thevoltage command may be arbitrarily set at such a magnitude that does notcause a sudden change in the current. When a current controller isprovided, 50% of the rated current is applied as the current command.Then, at the time the detected current value matches the current commandvalue, the current command value at this time may be set to V1. When theprimary resistance is measured with a DC current applied therefor beforeidentification of the mutual inductance or no-load current described inthe present invention, a current value and a voltage command value atthat time may be used. Of course, the current value may be set at avalue other than 50% of the rated current.

Next, V1 is applied as voltage command v_ref, and induction motor 3 isapplied with a voltage stepwise. Primary current i1 is measured at thistime, and îm is calculated in accordance with the aforementionedEquation (15). Here, in Equation (15), v corresponds to v_ref, and im toîm. Values used for R1, R2 are given by a test result table of theinduction motor or another existent identifying means.

Time constant τ is determined from the waveform of rising îm, and thevalue at this time is designated by {circumflex over (τ)}_(im).{circumflex over (τ)}m is substituted into τ shown in Equation (12) tocalculate mutual inductance M. While time constant {circumflex over(τ)}m is generally determined by measuring a time for îm to reach fromzero to a final (convergence) value (1−1/e)≈0.632, measurements may bemade on a change in the current at an arbitrary current value and on atime during the change, and conversion may be made to match this timewith the time constant. In the latter case, measurements can be made ata plurality of points, thereby making it possible to reduce variationsby measuring several data and averaging the data.

A seventeenth embodiment will be described.

Since rated voltage Vrate and rated frequency frate of the inductionmotor are given in the specifications of the induction motor, no-loadcurrent I0 is calculated by substituting rated voltage Vrate and ratedfrequency frate, R1, L, R2 given by the test result table of theinduction motor or another existent identifying means, and M identifiedby the aforementioned method into Equation (19):

$\begin{matrix}{{I0} = \frac{Vrate}{\sqrt{{R1}^{2} + {\left( {2\pi\;{frate}} \right)^{2}\left( {L + M} \right)^{2}}}}} & (20)\end{matrix}$

When an error is tolerable to some degree, L and R1 may be omitted inthe calculation for simplification.

Next, an eighteenth embodiment will be described.

As discussed above, when a DC current is applied, the equivalent circuitof the induction motor can be regarded as having only the primaryresistance. Therefore, although the DC current transiently flows intothe secondary resistance immediately after the DC current is applied,the primary resistance alone exists when a sufficient time has elapsed,so that the voltage is given by:v=R1·i1_(∞)where i1∞îm {circumflex over (τ)}_(im) represents a current value towhich primary current value i1 converges. The aforementioned Equation(15) can be rewritten to:

$\begin{matrix}{{im} = {{i1} - {\frac{R1}{R2}\left( {{i1}_{\infty} - {i1}} \right)}}} & (21)\end{matrix}$

Here, because of an estimate, im is described as îm. Subsequently, acalculation is made in a manner similar to the aforementioned sixteenthembodiment. In doing so, since no-voltage value is used in thecalculation, the measurement can be made independently of a voltageaccuracy of the driving apparatus. When a value upon measurement of theprimary resistance is used in applying the voltage command as describedabove, the value used for i1∞ may be a current value which is read uponmeasurement of the resistance.

A nineteenth embodiment carries out the seventeenth embodiment using themethod of calculating îm in the eighteenth embodiment.

1. A method of measuring a motor constant for an induction motor in amotor vector control apparatus having a d-axis currentproportional-plus-integral controller which receives a current commandfor a d-axis component of a primary current of the induction motor and adetected current value of the d-axis component for controlling adeviation between said current command for the d-axis component and saiddetected current value of the d-axis component to reduce to zero; afirst adder for adding an output of said d-axis currentproportional-plus-integral controller and an arbitrary d-axis auxiliaryvoltage command value to derive a d-axis voltage command value; a q-axiscurrent proportional-plus-integral controller which receives a currentcommand for a q-axis component of the primary current of the inductionmotor and a detected current value of the q-axis component forcontrolling a deviation between said current command for the q-axiscomponent and said detected current value of the q-axis component toreduce to zero; a second adder for adding an output of said q-axiscurrent proportional-plus-integral controller and an arbitrary q-axisauxiliary voltage command value to derive a q-axis voltage commandvalue; and a power converter for calculating a magnitude v_ref and avoltage phase θv of a voltage command from the d-axis voltage commandvalue and the q-axis voltage command value, and converting a DC currentto a three-phase AC current based on the magnitude v_ref of said voltagecommand and the voltage phase θv of said voltage command to output thethree-phase AC current, said motor vector control apparatus beingconfigured to convert the induction motor to an equivalent circuit of athree-phase Y (star) connection for handling and controlling theinduction motor, said method comprising the steps of: applying a d-axiscurrent command value id_ref1 and a q-axis current command value iq_ref1previously set at arbitrary fixed values as first command values, andapplying the arbitrary d-axis auxiliary voltage command value vd_ref_cand the arbitrary q-axis auxiliary voltage command value vq_ref_c bothset at zero to operate said vector control apparatus; after the lapse ofa previously set first time, setting a proportional gain of the d-axiscurrent proportional-plus-integral controller and a proportional gain ofthe q-axis current proportional-plus-integral controller to zero, andafter the lapse of a previously set second time from this time, creatingthe voltage command:v_ref=√{square root over ((vd_ref² +vq_ref²))} from the d-axis voltagecommand vd_ref and the q-axis voltage command vq_ref, and creating thedetected current value:i _(—) fb=√{square root over ((id _(—) fb ² +iq _(—) fb ²))} from thed-axis detected current value id_fb and the q-axis detected currentvalue iq_fb; setting an average of v_ref and an average of i_fb recordedwithin an arbitrary time during the second time as first data v_ref1,i_fb1, respectively; returning the gains of both saidproportional-plus-integral controllers to original values, applying ad-axis current command value id_ref2 and a q-axis current command valueiq_ref2 previously set at arbitrary fixed values as second commandvalues, and applying the arbitrary d-axis auxiliary voltage commandvalue vd_ref_c and the arbitrary q-axis auxiliary voltage command valuevq_ref_c set at zero to operate said vector control apparatus; after thelapse of the previously set first time, setting the proportional gain ofthe d-axis current proportional-plus-integral controller and theproportional gain of the q-axis current proportional-plus-integralcontroller to zero, and after the lapse of the previously set secondtime from this time, calculating a primary resistance of the inductionmotor in accordance with:R1={(v_ref2−v_ref1)/√{square root over (3)}}/(i _(—) fb2−i _(—) fb1)using an average of v_ref and an average of i_fb stored within anarbitrary time during the second time as second data v_ref2, i_fb2,respectively, and calculating a line-to-line resistance value of theinduction motor in accordance with R_(L-L)=2·R1.
 2. The method accordingto claim 1, including, after the lapse of the first time: setting theoutput of the d-axis current proportional-plus-integral controller tothe arbitrary d-axis auxiliary voltage command value, and simultaneouslysetting the proportional gain and integral gain of the d-axis currentproportional-plus-integral controller and the output of the d-axiscurrent proportional-plus-integral controller to zero; and setting theoutput of the q-axis current proportional-plus-integral controller tothe arbitrary q-axis auxiliary voltage command value, and simultaneouslysetting the proportional gain and integral gain of the q-axis currentproportional-plus-integral controller and the output of the q-axiscurrent proportional-plus-integral controller to zero.
 3. The methodaccording to claim 1, wherein three or more levels are provided for thed-axis current command value and the q-axis current command valuepreviously set at arbitrary fixed values, and the primary resistance iscalculated as an average of the values of the primary resistancecalculated in respective intervals.
 4. A method of measuring a motorconstant for an induction motor in a motor vector control apparatushaving a d-axis current proportional-plus-integral controller whichreceives a current command for a d-axis component of a primary currentof the induction motor and a detected current value of the d-axiscomponent for controlling a deviation between said current command forthe d-axis component and said detected current value of the d-axiscomponent to reduce to zero; a first adder for adding an output of saidd-axis current proportional-plus-integral controller and an arbitraryd-axis auxiliary voltage command value to derive a d-axis voltagecommand value; a q-axis current proportional-plus-integral controllerwhich receives a current command for a q-axis component of the primarycurrent of the induction motor and a detected current value of theq-axis component for controlling a deviation between said currentcommand for the q-axis component and said detected current value of theq-axis component to reduce to zero; a second adder for adding an outputof said q-axis current proportional-plus-integral controller and anarbitrary q-axis auxiliary voltage command value to derive a q-axisvoltage command value; and a power converter for calculating a magnitudev_ref and a voltage phase θv of a voltage command from the d-axisvoltage command value and the q-axis voltage command value, andconverting a DC current to a three-phase AC current based on themagnitude v_ref of said voltage command and the voltage phase θv of saidvoltage command to output the three-phase AC current, said vectorcontrol apparatus being configured to convert the induction motor to anequivalent circuit of a three-phase Y (star) connection for handling andcontrolling the induction motor, said method comprising the steps of:setting gains and outputs of both said proportional-plus-integralcontrollers, the arbitrary d-axis auxiliary voltage command value andthe arbitrary q-axis auxiliary voltage command value to zero, settingthe voltage phase θv to a previously set arbitrary fixed value, andgiving a magnitude vref of the voltage command byv_ref=vamp·sin(2·π·fh·t), where fh is a frequency 1/10 or more as highas a rated operation frequency of the induction motor, and vamp is avoltage amplitude; incrementally or decrementally adjusting vamp whilemonitoring a current value i_fb such that:i _(—) fb=√{square root over ((id _(—) fb ² +iq _(—) fb ²))} calculatedfrom a d-axis detected current value id_fb and a q-axis detected currentvalue iq_fb reaches a previously arbitrarily set first set currentvalue; after i_fb reaches said first set current value, setting anaverage of an absolute value of the magnitude v_ref of the voltagecommand to v_ref_ave1, an average of an absolute value of the magnitudeof the detected current value i_fb to i_fb_ave1, and the phase of i_fbwith respect to v_ref to θdif1 after the lapse of an arbitrarily settime; adjusting vamp to reach a previously set second set current value,and setting the average of the absolute value of the magnitude v_ref ofthe voltage command to v_ref_ave2, the average of the absolute value ofthe magnitude of the detected current value i_fb to i_fb_ave2, and thephase of i_fb with respect to v_ref to θdif2 after the lapse of said settime; calculating:Zx={v_ref_ave2−V_ref_ave1)/√{square root over (3)}}/(i _(—) fb_ave2−i_(—) fb_ave1), θdif_(—) L=(θdif1+θdif2)/2,Zx _(—) r=Zx·cos θdif_(—) L,Zx _(—) i=Zx·sin θdif_(—) L, and from this,calculating a secondary resistance of the induction motor in accordancewith R2=Zx_r−R1, and a leakage inductance in accordance withL=Zx_i/(2·π·fh).
 5. The method according to claim 4, including adding aDC offset component v_ref_ofs to the voltage command value to apply thevoltage command expressed by v_ref=vamp·sin(2·π·fh·t)+v_ref_ofs, feedingthe detected current value i_fb to a high pass filter designed to filterout a DC component and pass a signal having an fh component therethroughto use an output of the high pass filter as new i_fb, feeding v_ref to ahigh pass filter having the same characteristics as that used for i_fb,and calculating the secondary resistance R2 and the leakage inductance Lof the induction motor in accordance with the three equations of Zx,θdif_L, and Zx_r using the output of the high pass filter as new v_ref.6. The method according to claim 5, including calculating the primaryresistance:R1={(v_ref_(—) dc2−v_ref_(—) dc2)/√{square root over (3)}}/(i _(—) fb_(—) dc2−i _(—) fb _(—) dc1) using an average v_ref_dc1 of the voltagecommand v_ref and an average i_fb_dc1 of the detected current value i_fbat the first set current value before the detected current value i_fb isfed to the high pass filter, and an average v_ref_dc2 of the voltagecommand v_ref and an average i_fb_dc2 of the detected current value i_fbat the second set current value before the detected current value i_fbis fed to the high pass filter, and calculating the secondary resistanceR2 using the first resistance value.
 7. A method of measuring a motorconstant for an induction motor in a motor vector control apparatushaving a d-axis current proportional-plus-integral controller whichreceives a current command for a d-axis component of a primary currentof the induction motor and a detected current value of the d-axiscomponent for controlling a deviation between said current command forthe d-axis component and said detected current value of the d-axiscomponent to reduce to zero; a first adder for adding an output of saidd-axis current proportional-plus-integral controller and an arbitraryd-axis auxiliary voltage command value to derive a d-axis voltagecommand value; a q-axis current proportional-plus-integral controllerwhich receives a current command for a q-axis component of the primarycurrent of the induction motor and a detected current value of theq-axis component for controlling a deviation between said currentcommand for the q-axis component and said detected current value of theq-axis component to reduce to zero; a second adder for adding an outputof said q-axis current proportional-plus-integral controller and anarbitrary q-axis auxiliary voltage command value to derive a q-axisvoltage command value; and a power converter for calculating a magnitudev_ref and a voltage phase θv of a voltage command from the d-axisvoltage command value and the q-axis voltage command value, andconverting a DC current to a three-phase AC current based on themagnitude v_ref of said voltage command and the voltage phase θv of saidvoltage command to output the three-phase AC current, said vectorcontrol apparatus being configured to convert the induction motor to anequivalent circuit of a three-phase Y (star) connection for handling andcontrolling the induction motor, said method comprising the steps of:setting gains and outputs of both said proportional-plus-integralcontrollers, the arbitrary d-axis auxiliary voltage command value andthe arbitrary q-axis auxiliary voltage command value to zero, setting avoltage phase θv to a previously set arbitrary fixed value, and giving amagnitude vref of the voltage command by v_ref=vamp·sin(2·π·f1·t), wheref1 is a frequency ⅕ or less as high as a rated operation frequency ofthe induction motor, and vamp, is a voltage amplitude; incrementally ordecrementally adjusting vamp while monitoring a current value i_fb suchthat:i _(—) fb=√{square root over ((id _(—) fb ² +iq _(—) fb ²))} calculatedfrom a d-axis detected current value id_fb and a q-axis detected currentvalue iq_fb reaches a previously arbitrarily set first set currentvalue; after i_fb reaches said first set current value, setting anaverage of an absolute value of the magnitude v_ref of the voltagecommand to v_ref_ave3, an average of an absolute value of the magnitudeof the detected current value i_fb to i_fb_ave3, and the phase of i_fbwith respect to v_ref to θdif3 after the lapse of a first arbitrary settime; adjusting vamp to reach a previously set second set current value,and setting the average of the absolute value of the magnitude v_ref ofthe current command to v_ref_ave4, the average of the absolute value ofthe magnitude of the detected current value i_fb to i_fb_ave4, and thephase of i_fb with respect to v_ref to θdif4 after the lapse of saidfirst set time; calculating:Zx2={v_ref_ave4−v_ref_ave3)/√{square root over (3})}/(i _(—) fb_ave4−i_(—) fb_ave3), θdif_(—) m=(θdif3+θdif4)/2,Zx _(—) r2=Zx·cos θdif_(—) m, and from this, calculating a mutualinductance of the induction motor in accordance with the followingequation:$M = {\frac{R2}{2 \cdot \pi \cdot {f1}} \cdot {\sqrt{\frac{{Zx\_ r2} - {R1}}{{R1} + {R2} - {Zx\_ r2}}}.}}$8. The method according to claim 7, including adding a DC offsetcomponent v_ref_ofs to the voltage command value to apply the voltagecommand expressed by v_ref=vamp·sin(2·π·f1·t)+v_ref_ofs, feeding thedetected current value i_fb to a high pass filter designed to filter outa DC component and pass a signal having an fh component therethrough touse an output of the high pass filter as new i_fb, feeding v_ref to ahigh pass filter having the same characteristics as that used for i_fb,and calculating the mutual inductance M of the induction motor inaccordance with said calculation equation using the output of the highpass filter as new v_ref.
 9. The method according to claim 8, includingcalculating the primary resistance:R1={(v_ref_(—) dc2−v_ref_(—) dc2)/√{square root over (3})}/(i _(—) fb_(—) dc2−i _(—) fb _(—) dc1) using an average v_ref_dc1 of the voltagecommand v_ref and an average i_fb_dc1 of the detected current value i_fbat the first set current value before the detected current value i_fb isfed to the high pass filter, and an average v_ref_dc2 of the voltagecommand v_ref and an average i_fb_(—dc)2 of the detected current valuei_fb at the second set current value before the detected current valuei_fb is fed to the high pass filter, and calculating the secondaryresistance R2 using the first resistance value.